---
# System prepended metadata

title: Week4

---

# Week4
![](https://i.imgur.com/SILwmCo.png)

![](https://i.imgur.com/Kx4wHKw.png)

![](https://i.imgur.com/vQ9PBxp.png)
![](https://i.imgur.com/u1oBcCO.png)

![](https://i.imgur.com/r3E8ez1.png)
Random Walk很像AR
Q:所以AR一樣是不平穩的嗎?!

------以下模擬-------phi 給0.4
![](https://i.imgur.com/W3mYMYW.png)

**Lag 2-3後就很平穩!!!**

------以下模擬-------phi 但phi 給1
![](https://i.imgur.com/D67sfk1.png)

**變異數無快速下降**


------以下模擬-------AR(2)
![](https://i.imgur.com/BMLUvvf.png)
**有收斂**

##### 結論
|phi|<1 才穩!
![](https://i.imgur.com/UBB3v0y.png)


第二段
![](https://i.imgur.com/BE5kYjy.png)


![](https://i.imgur.com/yUKsiaf.png)
證明

![](https://i.imgur.com/GpTAfqq.jpg)

證明平均數
![](https://i.imgur.com/ZZauWgd.png)
證明變異數
![](https://i.imgur.com/x16GZ48.png)

Autocovariance
![](https://i.imgur.com/ssCjZI4.png)

Autocorrelation
![](https://i.imgur.com/Pii06kU.png)

AR(1)證明
![](https://i.imgur.com/T6qVKsS.png)
![](https://i.imgur.com/4vvZ85g.png)

結論
![](https://i.imgur.com/C4BguYB.png)



Yule-Walker-Equations


https://d3c33hcgiwev3.cloudfront.net/_abd6986bc2f9f05be40002e2ed403dec_Yule-Walker-Equations-2.pdf?Expires=1585785600&Signature=V5SjnAXzSVUJbwy6Uv7hZmaVmoZ1oAAuPixdq8rtb90S2XkXTVxXXdoGM8MHz9aEd1cDMObhsl57t4iMgT2apJ8dhF9xJNKoq53ks31kdxWMA3aM0ZQH6sXRH28u1-rcKXhXJCDhV4PSHj-7rLt2PgWpSj7ukt1pGGxUUB2wijU_&Key-Pair-Id=APKAJLTNE6QMUY6HBC5A
